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#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

const int N = 410;
const int INF = 1e9;

int d[N][N], k[N][N], n;
vector<int> g[N];

bool check(int m) {
    for (int x=1; x<=n; ++x) {
        for (int y=1; y<=n; ++y) {
            if (d[x][y] > m) {
                g[x].push_back(y);
            }
        }
    }

    for (int x=1; x<=n; ++x) {
        for (int v=1; v<=n; ++v) {
            k[x][v] = -INF;
            for (auto y : g[x]) {
                k[x][v] = max(k[x][v], d[v][y]);
            }
        }
    }

    for (int v=1; v<=n; ++v) {
        for (int u=v+1; u<=n; ++u) {
            bool ok = true;
            for (int x=1; x<=n; ++x) {
                if (d[x][u] >= d[x][v]) {
                    if (k[x][u] > m-d[x][v]) {
                        ok = false;
                        break;
                    }
                } else {
                    if (k[x][v] > m-d[x][u]) {
                        ok = false;
                        break;
                    }
                }
            }

            if (ok) return true;
        }
    }

    for (int i=1; i<=n; ++i) g[i].clear();

    return false;
}

void solve() {
    cin>>n;
    for (int i=1; i<=n; ++i) {
        string s; cin>>s;
        for (int j=1; j<=n; ++j) {
            if (s[j-1] == '1') d[i][j] = 1;
            else d[i][j] = INF;
        }

        d[i][i] = 0;
    }

    for (int k=1; k<=n; ++k) {
        for (int i=1; i<=n; ++i) {
            for (int j=1; j<=n; ++j) {
                d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }

    int l=1, r = n, ans = n;
    while (l <= r) {
        int m = (l+r)/2;
        if (check(m)) {
            r=m-1;
            ans = m;
        } else {
            l = m+1;
        }
    } cout<<ans<<"\n";

    for (int i=0; i<=n; ++i) g[i].clear();
    for (int i=0; i<=n; ++i) {
        for (int j=0; j<=n; ++j) k[i][j] = 0, d[i][j] = 0;
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    cout.tie(NULL);

    int t=1; cin>>t;
    while (t--) solve();
}